It is expected
[omano@omano-nvme ~]$ cat /usr/bin/fgrep
#!/bin/sh
cmd=${0##*/}
echo "$cmd: warning: $cmd is obsolescent; using grep -F" >&2
exec grep -F "$@"
So every program using fgrep will get this warning. It is not an issue as far as I understand. Google the message, it will have plenty of results from plenty of programs.
For this specific message while doing update-grub it is not in grub-mkconfig script, probably in one of the tools it uses. Anyway it has to be changed from each application using fgrep to grep -F but for now we’ll see this harmless warning.